Abstract: A Green's function-integral equation technique is used to obtain a numerical solution to the two-dimensional Dirichlet problem for the multiply connected region between the ground fines at and and exterior to the circular conductors with arbitrarily spaced centers and radii . If the smallest distance between each pair of conducting surfaces exceeds .1, the capacitance matrix for this system of conductors can be calculated to 6-place accuracy at a cost of about 15 seconds on the IBM 7044 computer.